My daughter was diagnosed with appendicitis. Is this likely to be a big problem for her?

Usually not. Most times, appendicitis can be treated laparoscopically with hospital stays from a few hours to a day or two. Ruptured appendicitis is much more serious and may require prolonged operations, other procedures, and rarely very serious complications.
No. Not if she is treated surgically. If she did not get surgery but only received antibiotics, then there is a chance it will happen again.